You can carry locked n cocked, which gets around the issue. For me, I kinda like the hard - military like trigger for home defense. You have to want to pull it.
If you can't hang w it as is - send it back to HK for a LEM conversion specify what you want. Several police agencies have 8-10lb triggers to protect "everyone"
Snap caps are an easy way to "wear-in" and get used to, your triggers unique pull.
Remember the old Walther PP, PPK or CZ50 ? Same issue and people simply adapted.
Have you ever watched doubles in skeet ? Done right, the recoil from the first shot sets you up to take the second. Doesn't always work out that way but I was wondering if you could work that out w a trigger drill ?
Anyone tried it ?